Watie was the leader of the so-called Southern Cherokee and was elected Principal Chief of the Cherokee (technically just the Southern faction) in 1862, after the defection/exodus of Principal Chief John Ross.
McCulloch authorized Watie to raise a battalion and appointed him colonel before the Cherokee Nation allied itself with the Confederacy. Watie was later authorized to raise a regiment which is known by various names but most commonly the 1st Cherokee Mounted Volunteers or just "Watie's Regiment". The regiment was predominently Cherokee citizens but also included citizens of Missouri and Arkansas. In 1863, the 2nd Cherokee Mtd Vols (Adair's Regt) was organized and ultimately Watie was promoted to brigadier general commanding the two Cherokee regiment and some other Indian units.
I am not aware of any evidence that Watie in person was at Wilson's Creek, Lexington, or Cane Hill. There was some number of Cherokee at Wilson's Creek and (correct me if I'm wrong) I understand that Quantrill accompanied this 'company' of Cherokee to Wilson's Creek. Watie's Regiment was often active in southwest Missouri (Neosho, Sherwood, Newtonia) and cooperated with Livingston, Quantrill, and Coffee.
Drew's Regiment, the 1st Cherokee Mounted Rifles, was organized at the signing of the Confederate Treaty. Both Drew's and Watie's regiments fought at Pea Ridge (Leetown) AR. In July 1862, Drew's Regiment defected to the Union and filled out the 2nd Indian Home Guard (IHG) Regiment and formed the 3rd IHG. The 1st IHG was predominately Muscogee (Creek). The three IHG regiments are commonly called the Union Indian Brigade.
The Cherokee IHG were encamped near Neosho MO with their families prior to the Prairie Grove campaign. The IHG fought a Prairie Grove and other engagements in Missouri, Arkansas, and Indian Territory.
There were other Confederate Indian Regiments organized in the Indian Territory (Choctaw, Chickasaw, Creek, Seminole) and, like you said, there were small numbers of Native Americans serving in units across the country.